import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

%matplotlib inline

from mpl_toolkits import mplot3d

Batch ,Stochastic and mini Gradient Descent¶

feature=pd.read_csv('training_feature_matrix.csv')

feature.mean()

f_1      -1.420408
f_2    1326.666667
dtype: float64

feature.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 245 entries, 0 to 244
Data columns (total 2 columns):
f_1    245 non-null float64
f_2    245 non-null float64
dtypes: float64(2)
memory usage: 3.9 KB

output=pd.read_csv('training_output.csv')

output.mean()

output    16.960068
dtype: float64

feature=pd.read_csv('training_feature_matrix.csv')

feature['constant']=1
features=['f_1','f_2']
features=['constant']+features
feature=feature[features]
feature

def feature_normalize(data):
    data=(data-data.mean())/data.std()
    return data

def cost_function(feature,weights,output):
    cost=0
    cost_half=0
    
    m=feature.shape[0]
    n=feature.shape[1]
    y_hat=np.zeros(m)
    for i in range(m):
        y_hat=0
        for j in range(n):
            
            y_hat+=weights[j]*feature[i][j]
        error=output[i]-y_hat
        cost_half+=error*error
    cost=(0.5*cost_half)/m
    
    return cost

def bgd(feature,output,alpha,iteration,weights):
    m=feature.shape[0]
    n=feature.shape[1]
    feature=feature.to_numpy()
    output=output.to_numpy()
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                gradient[j]+=error*feature[i][j]
            
        for j in range(n):
            temp[j]=temp[j]+(alpha*gradient[j])/m
        weights=temp
        
        v_1[it]=weights[0]
        v_2[it]=weights[1]
        v_3[it]=weights[2]
        cost[it]=cost_function(feature,weights,output)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

def sgd(feature,output,alpha,iteration,weights):
    m=feature.shape[0]
    n=feature.shape[1]
    feature=feature.to_numpy()
    output=output.to_numpy()
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            temp=weights
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                gradient[j]=error*feature[i][j]
            
            for j in range(n):
                temp[j]=temp[j]+(alpha*gradient[j])
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=cost_function(feature,weights,output)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

def mbgd(feature,output,alpha,iteration,weights,x):
    m=feature.shape[0]
    n=feature.shape[1]
    feature=feature.to_numpy()
    output=output.to_numpy()
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range((m-x)/10):
            temp=weights
            gradient=np.zeros(n)
            i=i*x
            for z in range(i,i+x):
                y_hat=0
                for j in range(n):
                    
                    y_hat+=temp[j]*feature[z][j]
                error=output[z]-y_hat
                for j in range(n):
                    gradient[j]+=error*feature[z][j]

            for j in range(n):
                temp[j]=temp[j]+(alpha*gradient[j])/x
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=cost_function(feature,weights,output)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

output=pd.read_csv('training_output.csv')

weights=np.zeros(3)
(weights,cost)=mbgd(feature,output,0.0001,1000,weights,5)
print weights

[-3.25619185 -3.28134978  8.45062871]

weights=np.zeros(3)
(weights,cost)=sgd(feature,output,0.001,1000,weights)
print weights

[-11.14600013  -6.81512766   3.29885439]

weights=np.zeros(3)
(weights,cost)=bgd(feature,output,0.001,1000,weights)
print weights

[-2.94154358 -2.96836707  8.41814008]

def predict(feature,weights,output):
    m=feature.shape[0]
    n=feature.shape[1]
    error_square=0
    for i in range(m):
        y_hat=0
        for j in range(n):
            y_hat+=weights[j]*feature[i][j]
        
        error_square+=(y_hat-output[i])**2
    error=error_square/m
    return error

test_feature=pd.read_csv('test_feature_matrix.csv')
test_output=pd.read_csv('test_output.csv')
test_feature['constant']=1
features=['f_1','f_2']
features=['constant']+features
test_feature=test_feature[features]
test_feature
feature=test_feature.to_numpy()
output=test_output.to_numpy()
feature=feature_normalize(feature)

print(predict(feature,weights,output))

[42.48592152]

Batch ,Stochastic and mini Gradient Descent using ridge regression :>¶

def cost_function(feature,weights,output,l_2):
    cost=0
    cost_half=0
    
    m=feature.shape[0]
    n=feature.shape[1]
    y_hat=np.zeros(m)
    for i in range(m):
        y_hat=0
        x=0
        for j in range(n):
            
            y_hat+=weights[j]*feature[i][j]
            x+=l_2*(weights[j]**2)
        error=output[i]-(y_hat)
        cost_half+=error*error+x
    cost=(0.5*cost_half)/m
    
    return cost

def bgd(feature,output,alpha,iteration,weights,reg_cons):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            x=0
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                x+=reg_cons*temp[j]
                gradient[j]+=error*feature[i][j]+x
            
        for j in range(n):
            temp[j]=temp[j]+(alpha*gradient[j])/m
        weights=temp
        
        v_1[it]=weights[0]
        v_2[it]=weights[1]
        v_3[it]=weights[2]
        cost[it]=cost_function(feature,weights,output,reg_cons)
    
    plt.plot(cost)
    
    

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=bgd(feature,output,0.00001,500,weights,0.001)
print weights

[0.96660572 0.96468153 1.0683475 ]

def sgd(feature,output,alpha,iteration,weights,reg_cons):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            x=0
            temp=weights
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                x+=reg_cons*temp[j]
                gradient[j]=error*feature[i][j]
            
            for j in range(n):
                temp[j]=temp[j]+(alpha*gradient[j])
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=cost_function(feature,weights,output,reg_cons)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=sgd(feature,output,0.0001,1000,weights,0.1)
print weights

[-3.25039382 -3.61068024  3.73714297]

def mbgd(feature,output,alpha,iteration,weights,x,reg_cons):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range((m-x)/10):
            temp=weights
            gradient=np.zeros(n)
            i=i*x
            y=0
            for z in range(i,i+x):
                y_hat=0
                for j in range(n):
                    
                    y_hat+=temp[j]*feature[z][j]
                error=output[z]-y_hat
                for j in range(n):
                    y+=reg_cons*temp[j]
                    gradient[j]+=error*feature[z][j]

            for j in range(n):
                temp[j]=temp[j]+(alpha*gradient[j])/x
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=cost_function(feature,weights,output,reg_cons)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=mbgd(feature,output,0.0001,500,weights,5,0.001)
print weights

[-0.47248896 -0.53106889  4.12545311]

def predict(feature,weights,output):
    m=feature.shape[0]
    n=feature.shape[1]
    error_square=0
    for i in range(m):
        y_hat=0
        for j in range(n):
            y_hat+=weights[j]*feature[i][j]
        
        error_square+=(y_hat-output[i])**2
    error=error_square/m
    return error

test_feature=pd.read_csv('test_feature_matrix.csv')
test_output=pd.read_csv('test_output.csv')
test_feature['constant']=1
features=['f_1','f_2']
features=['constant']+features
test_feature=test_feature[features]
test_feature
feature=test_feature.to_numpy()
output=test_output.to_numpy()
feature=feature_normalize(feature)

print(predict(feature,weights,output))

[18.14545105]

Derivation of least angle Regression¶

Least angle regression¶

def lar_cost_function(feature,weights,output,l_1):
    cost=0
    cost_half=0
    
    m=feature.shape[0]
    n=feature.shape[1]
    y_hat=np.zeros(m)
    
    for i in range(m):
        y_hat=0
        x=0
        for j in range(n):
            
            y_hat+=weights[j]*feature[i][j]
            x+=l_1*weights[j]
        error=output[i]-y_hat
        cost_half+=error*error
    cost=((0.5*cost_half)/m)+x/2
    
    return cost

def lar_bgd(feature,output,alpha,iteration,weights,l_1):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    x=0
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                gradient[j]+=error*feature[i][j]
                x+=l_1*np.sign(weights[j])
            
        for j in range(n):
            temp[j]=temp[j]+(alpha*(gradient[j]+x))/m
        weights=temp
        
        v_1[it]=weights[0]
        v_2[it]=weights[1]
        v_3[it]=weights[2]
        cost[it]=lar_cost_function(feature,weights,output,l_1)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=lar_bgd(feature,output,0.0001,1000,weights,0.001)
print weights

[0.56369731 0.52928599 2.33934225]

def lar_sgd(feature,output,alpha,iteration,weights,l_1):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    x=0
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range(m):
            y_hat=0
            temp=weights
            x=0
            for j in range(n):
                y_hat+=temp[j]*feature[i][j]
            error=output[i]-y_hat
            for j in range(n):
                gradient[j]=error*feature[i][j]
                x+=l_1*np.sign(weights[j])
            for j in range(n):
                temp[j]=temp[j]+(alpha*(gradient[j]+x))
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=lar_cost_function(feature,weights,output,l_1)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=lar_sgd(feature,output,0.0001,1000,weights,0.1)
print weights

[-4.03409769 -4.30942375  3.03465104]

def lar_mbgd(feature,output,alpha,iteration,weights,x,l_1):
    m=feature.shape[0]
    n=feature.shape[1]
    
    feature=feature_normalize(feature)
    cost=np.zeros(iteration)
    weights=np.ones(n)
    v_1= np.zeros(iteration)
    v_2= np.zeros(iteration)
    v_3= np.zeros(iteration)
    y=np.zeros(m)
    for it in range(iteration):
        temp=weights
        
        gradient=np.zeros(n)
        for i in range((m-x)/10):
            temp=weights
            gradient=np.zeros(n)
            i=i*x
            for z in range(i,i+x):
                y_hat=0
                l=0
                for j in range(n):
                    
                    y_hat+=temp[j]*feature[z][j]
                error=output[z]-y_hat
                for j in range(n):
                    gradient[j]+=error*feature[z][j]
                    l+=l_1*np.sign(weights[j])
            for j in range(n):
                temp[j]=temp[j]+(alpha*(gradient[j]+l))/x
            weights=temp
        
            v_1[i]=weights[0]
            v_2[i]=weights[1]
            v_3[i]=weights[2]
        cost[it]=lar_cost_function(feature,weights,output,l_1)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot3D(v_1,v_2,v_3,'gray')
    ax.set_title('3D line plot')
    plt.show()
    
    plt.plot(cost)

    return (weights,cost)

weights=np.zeros(3)
(weights,cost)=lar_mbgd(feature,output,0.0001,1000,weights,10,0.01)
print weights

[-1.23428324 -1.39161176  5.17478029]

Vectorized regression¶

def vect_cost_function(feature,weights,output):
    m=feature.shape[0]
    y_hat=np.dot(np.transpose(weights),np.transpose(feature))
    error=y_hat-output
    cost=(0.5*np.dot(np.transpose(error),error))/m
    return cost,error

def vect_bgd(feature,output,weights):
    m=feature.shape[0]
    
    part_1=np.dot(np.transpose(feature),feature)
    part_2=np.linalg.inv(part_1)
    part_3=np.dot(part_2,np.transpose(feature))
    weights=np.dot(part_3,output)
    cost=vect_cost_function(feature,weights,output)
    
    return weights,cost

weights=np.zeros(3)
(weights,cost)=vect_bgd(feature,output,weights)
print weights

[[-12.33563725]
 [ -1.01064465]
 [  0.80470535]]

def vect_cost_function(feature,weights,output,l):
    m=feature.shape[0]
    y_hat=np.dot(np.transpose(weights),np.transpose(feature))
    error=y_hat-output
    cost=((0.5*np.dot(np.transpose(error),error))/m)+(l*np.dot(np.transpose(weights),weights))/2
    return cost,error

def vect_ridge(feature,output,weights,l):
    m=feature.shape[0]
    
    part_1=np.dot(np.transpose(feature),feature)+l
    part_2=np.linalg.inv(part_1)
    part_3=np.dot(part_2,np.transpose(feature))
    weights=np.dot(part_3,output)
    cost=vect_cost_function(feature,weights,output,l)
    
    return weights,cost

weights=np.zeros(3)
(weights,cost)=vect_ridge(feature,output,weights,0.01)
print weights

[[-12.26025281]
 [ -1.03271882]
 [  0.82877599]]

def vect_cost_function(feature,weights,output,l_1):
    
    m=feature.shape[0]
    y_hat=np.dot(np.transpose(weights),np.transpose(feature))
    
    error=y_hat-output
    cost=((0.5*np.dot(np.transpose(error),error))/m)+(l_1*weights)/2
    return cost,error

def vect_lar(feature,output,weights,l_1):
    m=feature.shape[0]
    
    part_1=np.dot(np.transpose(feature),feature)
    part_2=np.linalg.inv(part_1)
    part_3=np.dot(np.transpose(feature),output)-(l_1*np.sign(weights)*0.5)
    
    weights=np.dot(part_2,part_3)
    print weights
    cost=vect_cost_function(feature,weights,output,l_1)
    plt.plot(cost)
    return weights

weights=np.ones(3)
(weights,cost)=vect_lar(feature,output,weights,0.1)
print weights

Least angle regression have low rmse as compared to linear regression

Logistic Regression¶

df=pd.read_csv('data3.csv')

df

df = pd.DataFrame(df) 
df.insert(0, "constant", [1]*100, True) 
df

train=df.sample(frac=0.6,random_state=200) #random state is a seed value
test=df.drop(train.index)
train['t'] = (train['t'] < 2)*1
train=train.to_numpy()
train

array([[1. , 4.9, 3.1, 1.5, 0.1, 1. ],
       [1. , 4.7, 3.2, 1.3, 0.2, 1. ],
       [1. , 6.3, 2.5, 4.9, 1.5, 0. ],
       [1. , 4.9, 3.1, 1.5, 0.1, 1. ],
       [1. , 6.7, 3.1, 4.7, 1.5, 0. ],
       [1. , 5.6, 2.9, 3.6, 1.3, 0. ],
       [1. , 5.5, 2.4, 3.8, 1.1, 0. ],
       [1. , 6.1, 2.9, 4.7, 1.4, 0. ],
       [1. , 4.9, 3.1, 1.5, 0.1, 1. ],
       [1. , 5.1, 3.8, 1.5, 0.3, 1. ],
       [1. , 4.5, 2.3, 1.3, 0.3, 1. ],
       [1. , 5.4, 3.7, 1.5, 0.2, 1. ],
       [1. , 5. , 2.3, 3.3, 1. , 0. ],
       [1. , 5.1, 3.8, 1.6, 0.2, 1. ],
       [1. , 5.3, 3.7, 1.5, 0.2, 1. ],
       [1. , 5.6, 3. , 4.1, 1.3, 0. ],
       [1. , 5. , 2. , 3.5, 1. , 0. ],
       [1. , 5.1, 3.8, 1.9, 0.4, 1. ],
       [1. , 5. , 3.5, 1.6, 0.6, 1. ],
       [1. , 4.3, 3. , 1.1, 0.1, 1. ],
       [1. , 5.1, 3.4, 1.5, 0.2, 1. ],
       [1. , 6. , 3.4, 4.5, 1.6, 0. ],
       [1. , 5.1, 3.5, 1.4, 0.3, 1. ],
       [1. , 4.6, 3.2, 1.4, 0.2, 1. ],
       [1. , 5.2, 3.4, 1.4, 0.2, 1. ],
       [1. , 5.6, 3. , 4.5, 1.5, 0. ],
       [1. , 5.4, 3.9, 1.7, 0.4, 1. ],
       [1. , 6.7, 3. , 5. , 1.7, 0. ],
       [1. , 5.5, 3.5, 1.3, 0.2, 1. ],
       [1. , 4.4, 3. , 1.3, 0.2, 1. ],
       [1. , 6. , 2.9, 4.5, 1.5, 0. ],
       [1. , 6.6, 3. , 4.4, 1.4, 0. ],
       [1. , 6.4, 2.9, 4.3, 1.3, 0. ],
       [1. , 5.6, 2.7, 4.2, 1.3, 0. ],
       [1. , 4.7, 3.2, 1.6, 0.2, 1. ],
       [1. , 5.5, 2.3, 4. , 1.3, 0. ],
       [1. , 4.8, 3.1, 1.6, 0.2, 1. ],
       [1. , 5. , 3.5, 1.3, 0.3, 1. ],
       [1. , 5. , 3. , 1.6, 0.2, 1. ],
       [1. , 5.8, 2.7, 3.9, 1.2, 0. ],
       [1. , 6.7, 3.1, 4.4, 1.4, 0. ],
       [1. , 5.5, 2.4, 3.7, 1. , 0. ],
       [1. , 6.2, 2.9, 4.3, 1.3, 0. ],
       [1. , 5.7, 3.8, 1.7, 0.3, 1. ],
       [1. , 5. , 3.3, 1.4, 0.2, 1. ],
       [1. , 5. , 3.6, 1.4, 0.2, 1. ],
       [1. , 4.8, 3. , 1.4, 0.1, 1. ],
       [1. , 6.1, 2.8, 4. , 1.3, 0. ],
       [1. , 6.1, 3. , 4.6, 1.4, 0. ],
       [1. , 6.3, 2.3, 4.4, 1.3, 0. ],
       [1. , 5.7, 2.8, 4.1, 1.3, 0. ],
       [1. , 6.6, 2.9, 4.6, 1.3, 0. ],
       [1. , 4.4, 2.9, 1.4, 0.2, 1. ],
       [1. , 5.5, 4.2, 1.4, 0.2, 1. ],
       [1. , 5.5, 2.6, 4.4, 1.2, 0. ],
       [1. , 5.6, 2.5, 3.9, 1.1, 0. ],
       [1. , 5.7, 3. , 4.2, 1.2, 0. ],
       [1. , 4.6, 3.1, 1.5, 0.2, 1. ],
       [1. , 5.1, 3.5, 1.4, 0.2, 1. ],
       [1. , 6.9, 3.1, 4.9, 1.5, 0. ]])

def sigmoid(x):
    y=(1/(1+np.exp(-x)))
    return y
x=np.linspace(-10,10,100)
y=sigmoid(x)
plt.plot(x,y)

[<matplotlib.lines.Line2D at 0x7fe012c74f10>]

fig=plt.figure(figsize=(8, 4))
ax=fig.add_subplot(111)
ax.plot(x, y, linewidth=2, color='#483d8b')

[<matplotlib.lines.Line2D at 0x7fe01285d6d0>]

fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(111)

# Colors for scatter points
colors = ['#483d8b', '#cc8400','#483d8b','#cc8400']

colors_data = [colors[int(i)] for i in y]

# Plot sample data
ax.scatter(train[:,2],train[:,1], color=colors_data, s=100, edgecolor='black', linewidth=2, alpha=0.7)

# Add grid
ax.grid(linestyle='--', linewidth=2, color='gray', alpha=0.2)

# Add axis labels


plt.show()

def feature_normalize(data):
    data=(data-data.mean())/data.std()
    return data

def cost_function(feature,output,weight):
    m=train.shape[0]
    n=(train.shape[1])-1
    cost=np.ones(m)
    cost_func=0
    for i in range(m):
        h=0
        for j in range(n):
            h+=weight[j]*feature[i][j]
        cost[i]=-((output[j])*np.log(sigmoid(h)))-((1-output[i])*np.log(1-sigmoid(h)))
    for k in range(m):
        cost_func+=cost[k]
    net_cost=cost_func/m
    return net_cost

def lgd(alpha,feature,output,weights,iteration):
    
    
    cost=np.ones(iteration)
    m=train.shape[0]
    n=(train.shape[1])-1
    weights=np.ones(n)
    feature=feature_normalize(feature)
    for it in range(iteration):
        temp=weights
        gradient=np.ones(n)
        for i in range(m):
            h=0
            for j in range(n):
                
                h+=temp[j]*feature[i][j]
            error=output[i]-h
            
            for j in range(n):
                gradient[j]+=error*feature[i][j]
                
        for j in range(n):
            temp[j]=temp[j]+(alpha*gradient[j])/m
        weights=temp
        
        cost[it]=cost_function(feature,output,weights)
    plt.plot(cost)
    return weights,cost

w=np.ones(5)
(weight,cost)=lgd(0.18,train[:,0:5],train[:,5],w,300)
print weight

[ 0.97075975  0.64224901  0.56826455 -0.63639474 -0.29859835]

test=test.to_numpy()

def predict(feature,weight):
    
    m=test.shape[0]
    n=(test.shape[1])-1
    predicted=np.zeros(m)
    y=np.zeros(m)
    
    for i in range(m):
        h=0
        for j in range(n):
            h+=weight[j]*feature[i][j]
        predicted[i]=sigmoid(h)
        print predicted[i]
        if(predicted[i]>=0.5):
            y[i]=2
        else:
            y[i]=1
        
    return y,predicted
    
y,predicted=(predict(test[:,0:5], weight))
print y

0.9923994210577672
0.992435325497122
0.9939389485507123
0.9926647624993494
0.9978614125396523
0.9976661785087471
0.9966929416168052
0.9946718730657397
0.9949069740164903
0.994906802135414
0.9925371901737333
0.9911353952171238
0.9931486412371083
0.9949588580345804
0.9950182132483409
0.9965153165905113
0.9943870941927807
0.9912339921347468
0.9916558589723274
0.9796846985623047
0.973088625512153
0.9664698714291089
0.9512358055042701
0.9684275537742012
0.9561824294414545
0.9500167522000698
0.9659100182102187
0.9619572145293099
0.9651860096325158
0.9474102896916826
0.9519515236849398
0.9581232705186002
0.9694232479091754
0.9729616121798069
0.9330927679717954
0.9443820180499675
0.952121854071142
0.9633638199665561
0.9615249502331116
0.968606229362932
[2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.
 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.]

m=40
true_positive=0
true_negative=0
false_positive=0
false_negative=0
for i in range(m):
    if(test[i,5]==y[i] and int(y[i])==2):
        true_negative+=1
    if(test[i,5]==y[i] and int(y[i])==1):
        true_positive+=1
    if(test[i,5]!=y[i] and int(y[i])==2):
        false_negative+=1
    if(test[i,5]!=y[i] and int(y[i])==1):
        false_positive+=1
sensitivity=(float(true_positive))/(true_positive+false_negative)
specificity=(float(true_negative))/(true_negative+false_positive)
accuracy=float(true_positive+true_negative)/m
print sensitivity,specificity,accuracy
print true_positive,true_negative,false_positive,false_negative

0.0 1.0 0.525
0 21 0 19

Multiclass regression¶

One vs all¶

data=pd.read_csv('data4 .csv')

data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
data

data

Output 1 vs 2 , 3¶

def sigmoid(x):
    y=(1/(1+np.exp(-x)))
    return y

train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)

train

train['output'] = (train['output'] < 2)*1

train

train=train.to_numpy()

train[:,6:8]=feature_normalize(train[:,6:8])

w=np.ones(8)
(weight,cost)=lgd(.1,train[:,0:8],train[:,8],w,250)
print weight,cost

[ 1.01898376  0.74961263  1.14674712 -0.49146472  0.18539606 -0.12893102
  0.60735951 -0.35990046] [1.11449987 0.97483258 0.86800399 0.78455894 0.7188427  0.66693832
 0.62588192 0.59334728 0.56749551 0.54687962 0.53036911 0.51708555
 0.50634819 0.49762939 0.49051913 0.48469754 0.47991372 0.47596974
 0.47270855 0.47000474 0.46775765 0.46588602 0.46432394 0.46301773
 0.46192347 0.46100511 0.46023301 0.45958266 0.45903381 0.45856966
 0.45817629 0.45784208 0.45755739 0.45731417 0.45710572 0.45692641
 0.45677158 0.45663731 0.45652033 0.45641789 0.4563277  0.45624784
 0.45617671 0.45611294 0.45605542 0.45600318 0.45595544 0.45591153
 0.45587088 0.45583303 0.45579758 0.45576419 0.45573258 0.45570252
 0.4556738  0.45564626 0.45561976 0.45559418 0.4555694  0.45554536
 0.45552196 0.45549916 0.45547689 0.45545511 0.45543378 0.45541286
 0.45539233 0.45537217 0.45535233 0.45533282 0.45531361 0.45529468
 0.45527602 0.45525763 0.45523948 0.45522157 0.45520388 0.45518642
 0.45516917 0.45515212 0.45513527 0.45511862 0.45510215 0.45508586
 0.45506975 0.45505381 0.45503803 0.45502242 0.45500696 0.45499166
 0.4549765  0.45496149 0.45494662 0.45493189 0.4549173  0.45490283
 0.4548885  0.45487429 0.4548602  0.45484623 0.45483237 0.45481864
 0.45480501 0.45479149 0.45477807 0.45476476 0.45475155 0.45473844
 0.45472543 0.45471251 0.45469968 0.45468694 0.45467429 0.45466173
 0.45464925 0.45463686 0.45462455 0.45461231 0.45460016 0.45458808
 0.45457607 0.45456414 0.45455228 0.45454049 0.45452876 0.45451711
 0.45450552 0.454494   0.45448254 0.45447114 0.45445981 0.45444853
 0.45443732 0.45442616 0.45441506 0.45440401 0.45439302 0.45438209
 0.4543712  0.45436037 0.4543496  0.45433887 0.45432819 0.45431756
 0.45430698 0.45429645 0.45428597 0.45427553 0.45426513 0.45425478
 0.45424448 0.45423422 0.454224   0.45421383 0.4542037  0.45419361
 0.45418356 0.45417355 0.45416358 0.45415365 0.45414376 0.45413391
 0.4541241  0.45411432 0.45410459 0.45409489 0.45408522 0.4540756
 0.45406601 0.45405645 0.45404693 0.45403745 0.454028   0.45401859
 0.4540092  0.45399986 0.45399055 0.45398127 0.45397202 0.45396281
 0.45395363 0.45394448 0.45393537 0.45392628 0.45391723 0.45390821
 0.45389922 0.45389027 0.45388134 0.45387245 0.45386359 0.45385475
 0.45384595 0.45383718 0.45382844 0.45381973 0.45381105 0.4538024
 0.45379378 0.45378518 0.45377662 0.45376809 0.45375959 0.45375111
 0.45374267 0.45373425 0.45372586 0.45371751 0.45370918 0.45370087
 0.4536926  0.45368436 0.45367614 0.45366796 0.4536598  0.45365167
 0.45364356 0.45363549 0.45362744 0.45361942 0.45361143 0.45360347
 0.45359553 0.45358762 0.45357974 0.45357189 0.45356406 0.45355626
 0.45354849 0.45354075 0.45353303 0.45352534 0.45351768 0.45351005
 0.45350244 0.45349486 0.4534873  0.45347978 0.45347228 0.4534648
 0.45345735 0.45344993 0.45344254 0.45343517 0.45342783 0.45342052
 0.45341323 0.45340597 0.45339874 0.45339153]

train
train[:,6:8]=feature_normalize(train[:,6:8])

h_hat=np.zeros(90)
for i in range(90):
    for j in range(8):
        h_hat[i]+=weight[j]*train[i][j]
    
fig=plt.figure(figsize=(9,8))
ax=fig.add_subplot(111)
colors = ['#483d8b', '#cc8400']
colors_data = [colors[int(i)] for i in train[:,8]]
ax.scatter(train[:,1],train[:,2], color=colors_data, s=100, edgecolor='black', linewidth=2, alpha=0.7)
ax.plot(h_hat, linewidth=2, color='#483d8b')
plt.xlim([4,8])
plt.ylim([1.5,3.9])

(1.5, 3.9)

3 vs 1, 2¶

data=pd.read_csv('data4 .csv')
data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)
train['output'] = (train['output'] >=3) * 1
train

train=train.to_numpy()

w=np.ones(8)
(weight,cost)=lgd(0.1,train[:,0:8],train[:,8],w,300)
print weight

[0.05114464 0.0562259  0.05366255 0.05398383 0.05137772 0.05285967
 0.08869747 0.19294561]

h_hat=np.zeros(90)
for i in range(90):
    for j in range(8):
        h_hat[i]+=weight[j]*train[i][j]
    
fig=plt.figure(figsize=(8, 4))
ax=fig.add_subplot(111)
colors = ['#483d8b', '#cc8400','red','green']
colors_data = [colors[int(i)] for i in train[:,8]]
ax.scatter(train[:,1],train[:,2], color=colors_data, s=100, edgecolor='black', linewidth=2, alpha=0.7)
ax.plot(h_hat, linewidth=2, color='#483d8b')
plt.xlim([4,8])
plt.ylim([1.7, 4])

(1.7, 4)

2 vs 1, 3¶

data=pd.read_csv('data4 .csv')
data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)
train['output'] = (train['output'] == 2) * 1
train

train=train.to_numpy()

train[:,6:8]=feature_normalize(train[:,6:8])

w=np.ones(8)
(weight,cost)=lgd(0.1,train[:,0:8],train[:,8],w,250)
print weight

[ 1.11309161  0.65358926  0.27029808  0.68066613  0.74529347 -0.87154425
  0.84683075 -0.66318167]

h_hat=np.zeros(90)
for i in range(90):
    for j in range(8):
        h_hat[i]+=weight[j]*train[i][j]
    
fig=plt.figure(figsize=(8, 4))
ax=fig.add_subplot(111)
colors = ['#483d8b', '#cc8400','red','green']
colors_data = [colors[int(i)] for i in train[:,8]]
ax.scatter(train[:,1],train[:,2], color=colors_data, s=100, edgecolor='black', linewidth=2, alpha=0.7)
ax.plot(h_hat, linewidth=2, color='#483d8b')
plt.xlim([4, 7.5])
plt.ylim([1, 3.9])

(1, 3.9)

test=test.to_numpy()

weight=[0.05114464, 0.0562259,  0.05366255, 0.05398383, 0.05137772, 0.05285967,
 0.08869747, 0.19294561]
def predict(feature,weight):
    
    m=test.shape[0]
    n=(test.shape[1])-1
    predicted=np.zeros(m)
    y=np.zeros(m)
    
    for i in range(m):
        h=0
        for j in range(n):
            h+=weight[j]*feature[i][j]
        predicted[i]=sigmoid(h)
        if(predicted[i]>=0.5):
            y[i]=1
        else:
            y[i]=0
        
    return y
    
y=(predict(test[:,0:8], weight))
print y

[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]

u1=0
u2=0
u3=0
for i in range(40):
    if(test[i,5]==y[i] and test[i,5]==1):
        u1+=1
    if(test[i,5]==y[i] and test[i,5]==2):
        u2+=1
    if(test[i,5]==y[i] and test[i,5]==3):
        u3+=1  
individual_acc_1=float(u1)/(u1+u2+u3)
individual_acc_2=float(u2)/(u1+u2+u3)
individual_acc_3=float(u3)/(u1+u2+u3)
overall_accuracy=float(u1+u2+u3)/40
print individual_acc_1,individual_acc_2,individual_acc_3
print overall_accuracy

1.0 0.0 0.0
0.05

One vs One¶

1 vs 2¶

data=pd.read_csv('data4 .csv')
data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)
train[train['output']==3]=0
train['output'] = (train['output'] >=2) * 1
train['output']
train

train=train.to_numpy()

w=np.ones(8)

(weight,cost)=lgd(0.1,train[:,0:8],train[:,8],w,300)
print weight

[0.02939423 0.03329167 0.02993446 0.03354443 0.03008265 0.03049143
 0.0199265  0.18541571]

J=1.08252153

2 vs 3¶

data=pd.read_csv('data4 .csv')
data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)
train[train['output']==1]=0
train['output'] = (train['output']==3) * 1
train['output']
train

train=train.to_numpy()

w=np.ones(8)

(weight,cost)=lgd(0.001,train[:,0:8],train[:,8],w,300)
print weight,cost

[0.94772753 0.94770872 0.94772514 0.94770891 0.94772054 0.9477029
 0.94753766 0.59298975] [0.33693372 0.33570091 0.3344807  0.33327296 0.33207755 0.33089437
 0.32972326 0.32856411 0.3274168  0.3262812  0.32515719 0.32404465
 0.32294346 0.3218535  0.32077466 0.31970681 0.31864985 0.31760367
 0.31656814 0.31554316 0.31452862 0.31352441 0.31253042 0.31154655
 0.31057269 0.30960874 0.30865459 0.30771015 0.30677531 0.30584997
 0.30493403 0.3040274  0.30312998 0.30224167 0.30136238 0.30049202
 0.29963049 0.2987777  0.29793356 0.29709798 0.29627088 0.29545215
 0.29464173 0.29383952 0.29304543 0.29225939 0.29148131 0.2907111
 0.28994869 0.289194   0.28844694 0.28770744 0.28697542 0.2862508
 0.28553351 0.28482346 0.28412059 0.28342483 0.28273609 0.28205431
 0.28137941 0.28071133 0.28004999 0.27939533 0.27874728 0.27810576
 0.27747071 0.27684208 0.27621978 0.27560375 0.27499394 0.27439028
 0.2737927  0.27320114 0.27261555 0.27203586 0.27146201 0.27089394
 0.27033159 0.26977491 0.26922383 0.2686783  0.26813827 0.26760368
 0.26707447 0.26655059 0.26603198 0.2655186  0.26501038 0.26450728
 0.26400925 0.26351623 0.26302817 0.26254503 0.26206675 0.26159328
 0.26112459 0.26066061 0.26020131 0.25974663 0.25929653 0.25885096
 0.25840988 0.25797325 0.25754101 0.25711313 0.25668956 0.25627026
 0.25585519 0.2554443  0.25503755 0.25463491 0.25423633 0.25384176
 0.25345118 0.25306455 0.25268181 0.25230294 0.2519279  0.25155664
 0.25118914 0.25082535 0.25046524 0.25010877 0.24975591 0.24940662
 0.24906087 0.24871861 0.24837983 0.24804448 0.24771253 0.24738395
 0.2470587  0.24673675 0.24641807 0.24610264 0.24579041 0.24548135
 0.24517544 0.24487264 0.24457293 0.24427628 0.24398265 0.24369201
 0.24340434 0.24311962 0.2428378  0.24255886 0.24228278 0.24200953
 0.24173908 0.24147141 0.24120648 0.24094427 0.24068476 0.24042791
 0.24017372 0.23992214 0.23967315 0.23942674 0.23918287 0.23894152
 0.23870267 0.23846629 0.23823237 0.23800087 0.23777178 0.23754506
 0.23732071 0.2370987  0.236879   0.23666159 0.23644646 0.23623357
 0.23602292 0.23581448 0.23560822 0.23540414 0.2352022  0.23500239
 0.23480469 0.23460907 0.23441553 0.23422403 0.23403457 0.23384712
 0.23366166 0.23347818 0.23329665 0.23311707 0.2329394  0.23276364
 0.23258976 0.23241776 0.2322476  0.23207928 0.23191278 0.23174807
 0.23158516 0.23142401 0.23126461 0.23110695 0.23095101 0.23079678
 0.23064423 0.23049336 0.23034414 0.23019658 0.23005064 0.22990631
 0.22976358 0.22962244 0.22948287 0.22934485 0.22920838 0.22907344
 0.22894001 0.22880808 0.22867765 0.22854868 0.22842118 0.22829512
 0.2281705  0.22804731 0.22792552 0.22780513 0.22768612 0.22756849
 0.22745222 0.22733729 0.22722371 0.22711144 0.22700049 0.22689084
 0.22678248 0.22667539 0.22656958 0.22646502 0.2263617  0.22625961
 0.22615875 0.2260591  0.22596066 0.2258634  0.22576732 0.22567241
 0.22557867 0.22548607 0.22539461 0.22530428 0.22521507 0.22512697
 0.22503997 0.22495406 0.22486923 0.22478547 0.22470277 0.22462113
 0.22454053 0.22446097 0.22438243 0.22430491 0.2242284  0.22415288
 0.22407836 0.22400482 0.22393225 0.22386065 0.22379001 0.22372031
 0.22365156 0.22358373 0.22351683 0.22345085 0.22338578 0.22332161
 0.22325833 0.22319593 0.22313442 0.22307377 0.22301399 0.22295507
 0.22289699 0.22283975 0.22278335 0.22272777 0.22267302 0.22261907
 0.22256593 0.2225136  0.22246205 0.22241129 0.22236131 0.2223121
 0.22226365 0.22221597 0.22216904 0.22212285 0.22207741 0.2220327 ]

j=0.2220327

1 vs 3¶

data=pd.read_csv('data4 .csv')
data = pd.DataFrame(data) 
data.insert(0, "constant", [1]*150, True) 
train=data.sample(frac=0.6,random_state=200) #random state is a seed value
test=data.drop(train.index)
train[train['output']==2]=0
train['output'] = (train['output']==3) * 1
train['output']
train

train=train.to_numpy()

w=np.ones(8)

(weight,cost)=lgd(0.001,train[:,0:8],train[:,8],w,300)
print weight,cost

[0.95180076 0.95183009 0.95184883 0.951732   0.95175638 0.95171087
 0.95250465 0.53636707] [0.19610408 0.19575006 0.19540014 0.19505427 0.1947124  0.1943745
 0.1940405  0.19371037 0.19338406 0.19306153 0.19274272 0.19242761
 0.19211614 0.19180827 0.19150396 0.19120318 0.19090587 0.190612
 0.19032153 0.19003443 0.18975064 0.18947014 0.18919288 0.18891884
 0.18864796 0.18838022 0.18811559 0.18785401 0.18759547 0.18733993
 0.18708735 0.18683769 0.18659094 0.18634704 0.18610598 0.18586772
 0.18563222 0.18539947 0.18516942 0.18494204 0.18471732 0.18449521
 0.18427569 0.18405873 0.1838443  0.18363237 0.18342293 0.18321593
 0.18301135 0.18280917 0.18260935 0.18241188 0.18221673 0.18202387
 0.18183328 0.18164493 0.1814588  0.18127487 0.18109311 0.18091349
 0.180736   0.18056061 0.1803873  0.18021605 0.18004683 0.17987962
 0.17971441 0.17955117 0.17938988 0.17923051 0.17907306 0.17891749
 0.17876379 0.17861195 0.17846193 0.17831372 0.1781673  0.17802265
 0.17787976 0.1777386  0.17759917 0.17746143 0.17732537 0.17719098
 0.17705823 0.17692712 0.17679762 0.17666971 0.17654339 0.17641863
 0.17629542 0.17617374 0.17605358 0.17593492 0.17581774 0.17570204
 0.17558779 0.17547498 0.1753636  0.17525364 0.17514507 0.17503788
 0.17493206 0.1748276  0.17472449 0.1746227  0.17452222 0.17442305
 0.17432517 0.17422857 0.17413323 0.17403914 0.17394629 0.17385467
 0.17376426 0.17367506 0.17358705 0.17350021 0.17341455 0.17333004
 0.17324667 0.17316444 0.17308333 0.17300334 0.17292444 0.17284663
 0.17276991 0.17269425 0.17261965 0.1725461  0.17247359 0.17240211
 0.17233164 0.17226219 0.17219373 0.17212626 0.17205978 0.17199426
 0.1719297  0.1718661  0.17180344 0.17174172 0.17168092 0.17162103
 0.17156206 0.17150398 0.17144679 0.17139049 0.17133506 0.1712805
 0.17122679 0.17117394 0.17112192 0.17107074 0.17102039 0.17097085
 0.17092213 0.17087421 0.17082708 0.17078074 0.17073518 0.1706904
 0.17064638 0.17060313 0.17056062 0.17051886 0.17047784 0.17043756
 0.17039799 0.17035915 0.17032102 0.17028359 0.17024686 0.17021083
 0.17017548 0.17014081 0.17010681 0.17007349 0.17004082 0.17000881
 0.16997745 0.16994674 0.16991666 0.16988722 0.1698584  0.1698302
 0.16980262 0.16977565 0.16974928 0.16972351 0.16969834 0.16967375
 0.16964975 0.16962632 0.16960347 0.16958118 0.16955946 0.16953829
 0.16951768 0.16949762 0.1694781  0.16945911 0.16944066 0.16942274
 0.16940535 0.16938847 0.1693721  0.16935625 0.1693409  0.16932606
 0.16931171 0.16929785 0.16928449 0.1692716  0.1692592  0.16924727
 0.16923581 0.16922482 0.1692143  0.16920423 0.16919462 0.16918546
 0.16917675 0.16916848 0.16916065 0.16915325 0.16914629 0.16913976
 0.16913365 0.16912796 0.1691227  0.16911784 0.16911339 0.16910936
 0.16910572 0.16910248 0.16909965 0.1690972  0.16909514 0.16909347
 0.16909219 0.16909128 0.16909075 0.16909059 0.16909081 0.16909139
 0.16909233 0.16909363 0.1690953  0.16909731 0.16909968 0.1691024
 0.16910547 0.16910887 0.16911262 0.1691167  0.16912112 0.16912587
 0.16913095 0.16913635 0.16914208 0.16914813 0.1691545  0.16916118
 0.16916817 0.16917547 0.16918309 0.169191   0.16919922 0.16920774
 0.16921655 0.16922566 0.16923506 0.16924475 0.16925473 0.169265
 0.16927554 0.16928637 0.16929747 0.16930886 0.16932051 0.16933243
 0.16934463 0.16935709 0.16936981 0.1693828  0.16939605 0.16940955
 0.16942332 0.16943733 0.1694516  0.16946611 0.16948088 0.16949589
 0.16951114 0.16952664 0.16954237 0.16955834 0.16957455 0.16959099]

j=0.16959099

As third case have least J it will be used to predict¶

h_hat=np.zeros(90)
weight=[0.95180076 ,0.95183009, 0.95184883, 0.951732,   0.95175638 ,0.95171087,
 0.95250465, 0.53636707]
for i in range(90):
    for j in range(8):
        h_hat[i]+=weight[j]*train[i][j]
    
fig=plt.figure(figsize=(8, 4))
ax=fig.add_subplot(111)
colors = ['#483d8b', '#cc8400','red','green']
colors_data = [colors[int(i)] for i in train[:,8]]
ax.scatter(train[:,1],train[:,2], color=colors_data, s=100, edgecolor='black', linewidth=2, alpha=0.7)
ax.plot(h_hat, linewidth=2, color='#483d8b')
plt.xlim([4, 7])
plt.ylim([0, 20])

(0, 20)

def predict(feature,weight):
    
    m=test.shape[0]
    n=(test.shape[1])-1
    predicted=np.zeros(m)
    y=np.zeros(m)
    
    for i in range(m):
        h=0
        for j in range(n):
            h+=weight[j]*feature[i][j]
        predicted[i]=sigmoid(h)
        if(predicted[i]>=0.5):
            y[i]=1
        else:
            y[i]=0
        
    return y

test=test.to_numpy()

for i in range(40):
    if(test[i,5]==y[i] and test[i,5]==1):
        u1+=1
    if(test[i,5]==y[i] and test[i,5]==2):
        u2+=1
    if(test[i,5]==y[i] and test[i,5]==3):
        u3+=1  
individual_acc_1=float(u1)/(u1+u2+u3)
individual_acc_2=float(u2)/(u1+u2+u3)
individual_acc_3=float(u3)/(u1+u2+u3)
overall_accuracy=float(u1+u2+u3)/40
print individual_acc_1,individual_acc_2,individual_acc_3
print overall_accuracy

1.0 0.0 0.0
0.1

Clustering¶

feature=pd.read_csv('data2.csv')

plt.scatter(feature['x1'],feature['x2'],feature['x3'],feature['x4'])

<matplotlib.collections.PathCollection at 0x7fe012b68b50>

from math import sqrt
import random
def feature_normalize(data):
    data=(data-data.mean())/data.std()
    return data

feature=feature.to_numpy()
def cluster(K,feature,iteration):
    #centroids=[[5, 3.4 ,1.5, 0.2], [6, 3 , 4 , 1.4] ,[7, 3, 6 ,2]]
    centroids=[(random.sample(range(-1,5), 4)),(random.sample(range(-1,5), 4)),(random.sample(range(-1,5), 4))]
    print centroids
    diff=[0,0,0]
    m=feature.shape[0]
    n=feature.shape[1]
    
    
    
    for it in range(iteration):
        
        clusters_1=[]
        clusters_2=[]
        clusters_3=[]
        c=0
        for i in range(m):
                
                for k in range(K):
                    diff[k]=sqrt(np.dot((feature[i]-centroids[k]),(feature[i]-centroids[k])))
                   
                c=diff.index(min(diff))
                        
                
                if(c==0):
                    (clusters_1).append(feature[i])
                elif (c==1):
                    (clusters_2).append(feature[i])
                else:
                    (clusters_3).append(feature[i])
                
        for k in range(K):
            if(k==0):
                centroids[k]=sum(clusters_1)/len(clusters_1)
            elif (k==1):
                centroids[k]=sum(clusters_2)/len(clusters_2)
            else:
                centroids[k]=sum(clusters_3)/len(clusters_3)
            
    len(clusters_2),len(clusters_3)
    
    return centroids,clusters_2,clusters_1,clusters_3

(centroids,cluster_2,cluster_1,clusters_3)=cluster(3,feature,1000)
print centroids

[[2, 1, 0, 3], [1, 4, 3, 0], [1, 4, 2, 3]]
[array([5.006, 3.418, 1.464, 0.244]), array([5.88360656, 2.74098361, 4.38852459, 1.43442623]), array([6.85384615, 3.07692308, 5.71538462, 2.05384615])]

fig= plt.figure(figsize=(10,9))

plt.scatter(5.006, 3.418, s=200, c='g', marker='s')
plt.scatter(5.88360656, 2.74098361, s=200, c='r', marker='s')
plt.scatter(6.85384615, 3.07692308, s=200, c='b', marker='s')


plt.scatter(feature[ : , 0], feature[ : , 1], s =50, c='g')
plt.scatter(feature[ : , 2], feature[ : , 3], s =50, c='g')
#blue red green squares represent the centroids

<matplotlib.collections.PathCollection at 0x7fe012ac7710>

Multiple regression using 5 hold cross validation¶

from random import seed
from random import randrange
from csv import reader
from math import exp
 
# Load a CSV file
def load_csv(filename):
    dataset = list()
    with open(filename, 'r') as file:
        csv_reader = reader(file)
        for row in csv_reader:
            if not row:
                continue
            dataset.append(row)
    return dataset
 
# Convert string column to float
def str_column_to_float(dataset, column):
    for row in dataset:
        row[column] = float(row[column].strip())
 
# Find the min and max values for each column
def dataset_minmax(dataset):
    minmax = list()
    for i in range(len(dataset[0])):
        col_values = [row[i] for row in dataset]
        value_min = min(col_values)
        value_max = max(col_values)
        minmax.append([value_min, value_max])
    return minmax
 
# Rescale dataset columns to the range 0-1
def normalize_dataset(dataset, minmax):
    for row in dataset:
        for i in range(len(row)):
            row[i] = (row[i] - minmax[i][0]) / (minmax[i][1] - minmax[i][0])
 
# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
    dataset_split = list()
    dataset_copy = list(dataset)
    fold_size = int(len(dataset) / n_folds)
    for i in range(n_folds):
        fold = list()
        while len(fold) < fold_size:
            index = randrange(len(dataset_copy))
            fold.append(dataset_copy.pop(index))
        dataset_split.append(fold)
    return dataset_split
 
# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
    correct = 0
    for i in range(len(actual)):
        if actual[i] == predicted[i]:
            correct += 1
    return correct / float(len(actual)) * 100.0
 
# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
    folds = cross_validation_split(dataset, n_folds)
    scores = list()
    for fold in folds:
        train_set = list(folds)
        train_set.remove(fold)
        train_set = sum(train_set, [])
        test_set = list()
        for row in fold:
            row_copy = list(row)
            test_set.append(row_copy)
            row_copy[-1] = None
        predicted = algorithm(train_set, test_set, *args)
        actual = [row[-1] for row in fold]
        accuracy = accuracy_metric(actual, predicted)
        scores.append(accuracy)
    return scores
 
# Make a prediction with coefficients
def predict(row, coefficients):
    yhat = coefficients[0]
    for i in range(len(row)-1):
        yhat += coefficients[i + 1] * row[i]
    return 1.0 / (1.0 + exp(-yhat))
 
# Estimate logistic regression coefficients using stochastic gradient descent
def coefficients_sgd(train, l_rate, n_epoch):
    coef = [0.0 for i in range(len(train[0]))]
    for epoch in range(n_epoch):
        for row in train:
            yhat = predict(row, coef)
            error = row[-1] - yhat
            coef[0] = coef[0] + l_rate * error * yhat * (1.0 - yhat)
            for i in range(len(row)-1):
                coef[i + 1] = coef[i + 1] + l_rate * error * yhat * (1.0 - yhat) * row[i]
    return coef
 
# Linear Regression Algorithm With Stochastic Gradient Descent
def logistic_regression(train, test, l_rate, n_epoch):
    predictions = list()
    coef = coefficients_sgd(train, l_rate, n_epoch)
    for row in test:
        yhat = predict(row, coef)
        yhat = round(yhat)
        predictions.append(yhat)
    return(predictions)
 
# Test the logistic regression algorithm 
seed(1)
# load and prepare data
filename = 'data4 .csv'

dataset = load_csv(filename)
dataset.pop(0)
for i in range(len(dataset[0])):
    str_column_to_float(dataset, i)
# normalize
minmax = dataset_minmax(dataset)
normalize_dataset(dataset, minmax)
# evaluate algorithm
n_folds = 5
l_rate = 0.1
n_epoch = 100
scores = evaluate_algorithm(dataset, logistic_regression, n_folds, l_rate, n_epoch)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))

Scores: [66.66666666666666, 70.0, 50.0, 66.66666666666666, 80.0]
Mean Accuracy: 66.667%

Likelihood ratio test¶

df=pd.read_csv("data3.csv")

df = pd.DataFrame(df) 
df.insert(0, "constant", [1]*100, True) 
df

train=df.sample(frac=0.6,random_state=200) #random state is a seed value
test=df.drop(train.index)
len(train)
train['t'] = (train['t'] < 2)*1
train=train.to_numpy()

len(test)

40

def sigmoid(x):
    y=(1/(1+np.exp(-x)))
    return y

def feature_normalize(data):
    data=(data-data.mean())/data.std()
    return data

def cost_function(feature,output,weight):
    m=train.shape[0]
    n=1
    cost=np.ones(m)
    cost_func=0
    for i in range(m):
        
        
        h=weight[0]*1
        cost[i]=-((output[i])*np.log(sigmoid(h)))-((1-output[i])*np.log(1-sigmoid(h)))
    for k in range(m):
        cost_func+=cost[k]
    net_cost=cost_func/m
    return net_cost

def lgd(alpha,feature,output,weights,iteration):
    
    
    cost=np.ones(iteration)
    m=train.shape[0]
    n=1
    weights=np.ones(n)
    
    for it in range(iteration):
        temp=weights
        gradient=np.ones(n)
        for i in range(m):
            
            
                
            h=temp[0]*1
            error=output[i]-h
            
            
            gradient[0]+=error*1
                
        
        temp[0]=temp[0]+(alpha*gradient[0])/m
        weights=temp
        
        cost[it]=cost_function(feature,output,weights)
    plt.plot(cost)
    return weights,cost

test=test.to_numpy()

from previous question log l=30.6¶

w=np.ones(5)
(weight,cost)=lgd(0.08,train[:,0],train[:,5],w,500)
print weight

[0.53333333]

2 log l = 87¶

Only intercept model is best¶

def predict(feature,weight):
    
    m=test.shape[0]
    n=1
    predicted=np.zeros(m)
    y=np.zeros(m)
    chi_sq=0
    h=0
    for i in range(m):
        h+=weight[0]*1
        predicted[i]=sigmoid(h)
        print predicted[i]
        if(predicted[i]>=0.5):
            y[i]=2
        else:
            y[i]=1
        chi_sq+=((predicted[i]-test[i,5])**2)/predicted[i]
    return y,predicted,chi_sq
    
y,predicted,chi_sq=(predict(test, weight))
print y,chi_sq

0.6302602229177514
0.7439624913247582
0.8320183851339248
0.8941010377640823
0.9350308308713361
0.9608342772032357
0.9766454835230229
0.9861656084433474
0.9918374288468401
0.9951952471128405
0.9971757006472715
0.9983411989198255
0.9990262029122943
0.9994284955764196
0.9996646498695336
0.9998032408393402
0.9998845625935888
0.9999322758503804
0.9999602687714186
0.9999766914421585
0.9999863259909154
0.9999919781489238
0.9999952939957882
0.9999972392350497
0.9999983804058309
0.9999990498705674
0.9999994426099414
0.9999996730091539
0.9999998081720304
0.9999998874648379
0.9999999339816695
0.999999961270595
0.9999999772795406
0.9999999866711282
0.9999999921806678
0.9999999954128183
0.9999999973089471
0.9999999984213039
0.9999999990738639
0.9999999994566857
[2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.
 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.] 21.358615549771724

m=40
true_positive=0
true_negative=0
false_positive=0
false_negative=0
for i in range(m):
    if(test[i,5]==y[i] and int(y[i])==2):
        true_negative+=1
    if(test[i,5]==y[i] and int(y[i])==1):
        true_positive+=1
    if(test[i,5]!=y[i] and int(y[i])==2):
        false_negative+=1
    if(test[i,5]!=y[i] and int(y[i])==1):
        false_positive+=1
sensitivity=(float(true_positive))/(true_positive+false_negative)
specificity=(float(true_negative))/(true_negative+false_positive)
accuracy=float(true_positive+true_negative)/m
print sensitivity,specificity,accuracy
print true_positive,true_negative,false_positive,false_negative

0.0 1.0 0.525
0 21 0 19

Maximum a Posterior Probability¶

# Naive Bayes 
from csv import reader
from random import seed
from random import randrange
from math import sqrt
from math import exp
from math import pi

# Load a CSV file
def load_csv(filename):
    dataset = list()
    with open(filename, 'r') as file:
        
        csv_reader = reader(file)
        for row in csv_reader:
            if not row:
                continue
            dataset.append(row)
    return dataset

# Convert string column to float
def str_column_to_float(dataset, column):
    for row in dataset:
        row[column] = float(row[column].strip())

# Convert string column to integer
def str_column_to_int(dataset, column):
    class_values = [row[column] for row in dataset]
    unique = set(class_values)
    lookup = dict()
    for i, value in enumerate(unique):
        lookup[value] = i
    for row in dataset:
        row[column] = lookup[row[column]]
    return lookup


# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
    correct = 0
    for i in range(len(actual)):
        if actual[i] == predicted[i]:
            correct += 1
    return correct / float(len(actual)) * 100.0

# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
    dataset_split = list()
    dataset_copy = list(dataset)
    fold_size = int(len(dataset) / n_folds)
    for _ in range(n_folds):
        fold = list()
        while len(fold) < fold_size:
            index = randrange(len(dataset_copy))
            fold.append(dataset_copy.pop(index))
        dataset_split.append(fold)
    return dataset_split


# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
    folds = cross_validation_split(dataset, n_folds)
    scores = list()
    for fold in folds:
        train_set = list(folds)
        train_set.remove(fold)
        train_set = sum(train_set, [])
        test_set = list()
        for row in fold:
            row_copy = list(row)
            test_set.append(row_copy)
            row_copy[-1] = None
        predicted = algorithm(train_set, test_set, *args)
        actual = [row[-1] for row in fold]
        accuracy = accuracy_metric(actual, predicted)
        scores.append(accuracy)
    return scores

# Split the dataset by class values, returns a dictionary
def separate_by_class(dataset):
    separated = dict()
    for i in range(len(dataset)):
        vector = dataset[i]
        class_value = vector[-1]
        if (class_value not in separated):
            separated[class_value] = list()
        separated[class_value].append(vector)
    return separated

# Calculate the mean of a list of numbers
def mean(numbers):
    return sum(numbers)/float(len(numbers))

# Calculate the standard deviation of a list of numbers
def stdev(numbers):
    avg = mean(numbers)
    variance = sum([(x-avg)**2 for x in numbers]) / float(len(numbers)-1)
    return sqrt(variance)

# Calculate the mean, stdev and count for each column in a dataset
def summarize_dataset(dataset):
    summaries = [(mean(column), stdev(column), len(column)) for column in zip(*dataset)]
    del(summaries[-1])
    return summaries

# Split dataset by class then calculate statistics for each row
def summarize_by_class(dataset):
    separated = separate_by_class(dataset)
    summaries = dict()
    for class_value, rows in separated.items():
        summaries[class_value] = summarize_dataset(rows)
    return summaries

# Calculate the Gaussian probability distribution function for x
def calculate_probability(x, mean, stdev):
    exponent = exp(-((x-mean)**2 / (2 * stdev**2 )))
    return (1 / (sqrt(2 * pi) * stdev)) * exponent

# Calculate the probabilities of predicting each class for a given row
def calculate_class_probabilities(summaries, row):
    total_rows = sum([summaries[label][0][2] for label in summaries])
    probabilities = dict()
    for class_value, class_summaries in summaries.items():
        probabilities[class_value] = summaries[class_value][0][2]/float(total_rows)
        for i in range(len(class_summaries)):
            mean, stdev, _ = class_summaries[i]
            probabilities[class_value]*= calculate_probability(row[i], mean, stdev)
    return probabilities

# Predict the class for a given row
def predict(summaries, row):
    probabilities = calculate_class_probabilities(summaries, row)
    best_label, best_prob = None, -1
    for class_value, probability in probabilities.items():
        if best_label is None or probability > best_prob:
            best_prob = probability
            best_label = class_value
    return best_label

# Naive Bayes Algorithm
def naive_bayes(train, test):
    summarize = summarize_by_class(train)
    predictions = list()
    for row in test:
        output = predict(summarize, row)
        predictions.append(output)
    return(predictions)

# Test Naive Bayes 
seed(1)
filename="data4 .csv"

dataset = load_csv(filename)
dataset.pop(0)
print(dataset[0])
for i in range(len(dataset[0])-1):
    str_column_to_float(dataset, i)
# convert class column to integers
str_column_to_int(dataset, len(dataset[0])-1)
# evaluate algorithm
n_folds = 2
scores = evaluate_algorithm(dataset, naive_bayes, n_folds)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))

['5.1', '3.5', '1.4', '0.2', '0.04', '44.275', '3455.15251', '1']
Scores: [94.66666666666667, 94.66666666666667]
Mean Accuracy: 94.667%

Maximum Likelihood Estimation Decision¶

# Naive Bayes 
from csv import reader
from random import seed
from random import randrange
from math import sqrt
from math import exp
from math import pi

# Load a CSV file
def load_csv(filename):
    dataset = list()
    with open(filename, 'r') as file:
        
        csv_reader = reader(file)
        for row in csv_reader:
            if not row:
                continue
            dataset.append(row)
    return dataset

# Convert string column to float
def str_column_to_float(dataset, column):
    for row in dataset:
        row[column] = float(row[column].strip())

# Convert string column to integer
def str_column_to_int(dataset, column):
    class_values = [row[column] for row in dataset]
    unique = set(class_values)
    lookup = dict()
    for i, value in enumerate(unique):
        lookup[value] = i
    for row in dataset:
        row[column] = lookup[row[column]]
    return lookup


# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
    correct = 0
    for i in range(len(actual)):
        if actual[i] == predicted[i]:
            correct += 1
    return correct / float(len(actual)) * 100.0

# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
    dataset_split = list()
    dataset_copy = list(dataset)
    fold_size = int(len(dataset) / n_folds)
    for _ in range(n_folds):
        fold = list()
        while len(fold) < fold_size:
            index = randrange(len(dataset_copy))
            fold.append(dataset_copy.pop(index))
        dataset_split.append(fold)
    return dataset_split


# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
    folds = cross_validation_split(dataset, n_folds)
    scores = list()
    for fold in folds:
        train_set = list(folds)
        train_set.remove(fold)
        train_set = sum(train_set, [])
        test_set = list()
        for row in fold:
            row_copy = list(row)
            test_set.append(row_copy)
            row_copy[-1] = None
        predicted = algorithm(train_set, test_set, *args)
        actual = [row[-1] for row in fold]
        accuracy = accuracy_metric(actual, predicted)
        scores.append(accuracy)
    return scores

# Split the dataset by class values, returns a dictionary
def separate_by_class(dataset):
    separated = dict()
    for i in range(len(dataset)):
        vector = dataset[i]
        class_value = vector[-1]
        if (class_value not in separated):
            separated[class_value] = list()
        separated[class_value].append(vector)
    return separated

# Calculate the mean of a list of numbers
def mean(numbers):
    return sum(numbers)/float(len(numbers))

# Calculate the standard deviation of a list of numbers
def stdev(numbers):
    avg = mean(numbers)
    variance = sum([(x-avg)**2 for x in numbers]) / float(len(numbers)-1)
    return sqrt(variance)

# Calculate the mean, stdev and count for each column in a dataset
def summarize_dataset(dataset):
    summaries = [(mean(column), stdev(column), len(column)) for column in zip(*dataset)]
    del(summaries[-1])
    return summaries

# Split dataset by class then calculate statistics for each row
def summarize_by_class(dataset):
    separated = separate_by_class(dataset)
    summaries = dict()
    for class_value, rows in separated.items():
        summaries[class_value] = summarize_dataset(rows)
    return summaries

# Calculate the Gaussian probability distribution function for x
def calculate_probability(x, mean, stdev):
    exponent = exp(-((x-mean)**2 / (2 * stdev**2 )))
    return (1 / (sqrt(2 * pi) * stdev)) * exponent

# Calculate the probabilities of predicting each class for a given row
def calculate_class_probabilities(summaries, row):
    total_rows = sum([summaries[label][0][2] for label in summaries])
    probabilities = dict()
    for class_value, class_summaries in summaries.items():
        probabilities[class_value] = summaries[class_value][0][2]/float(total_rows)
        for i in range(len(class_summaries)):
            mean, stdev, _ = class_summaries[i]
            probabilities[class_value]= calculate_probability(row[i], mean, stdev)
    return probabilities

# Predict the class for a given row
def predict(summaries, row):
    probabilities = calculate_class_probabilities(summaries, row)
    best_label, best_prob = None, -1
    for class_value, probability in probabilities.items():
        if best_label is None or probability > best_prob:
            best_prob = probability
            best_label = class_value
    return best_label

# Naive Bayes Algorithm
def naive_bayes(train, test):
    summarize = summarize_by_class(train)
    predictions = list()
    for row in test:
        output = predict(summarize, row)
        predictions.append(output)
    return(predictions)

# Test Naive Bayes 
seed(1)
filename="data4 .csv"

dataset = load_csv(filename)
dataset.pop(0)
print(dataset[0])
for i in range(len(dataset[0])-1):
    str_column_to_float(dataset, i)
# convert class column to integers
str_column_to_int(dataset, len(dataset[0])-1)
# evaluate algorithm
n_folds = 2
scores = evaluate_algorithm(dataset, naive_bayes, n_folds)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))

['5.1', '3.5', '1.4', '0.2', '0.04', '44.275', '3455.15251', '1']
Scores: [61.33333333333333, 68.0]
Mean Accuracy: 64.667%

Learning from assignment¶

I have learnt various operation on pandas like random splitting and adding columns etc. I have gained knowledge of algorithms and their implementations such as batch,stochastic and mini batch regression is used to get particular predicted value and with the help of rmse we can calculate error in prediction. Similary we can use logistic regression to predict yes or no based decision. Through clustering we can predict catagory of data with the help of centroids.And we can implement various probabilistic classifier also.

	constant	f_1	f_2
0	1	2.6	1360.00
1	1	2.0	1292.25
2	1	1.2	1185.00
3	1	2.0	1333.25
4	1	4.8	1580.75
5	1	3.1	1350.25
6	1	2.7	1262.75
7	1	2.1	1206.25
8	1	2.5	1251.50
9	1	2.7	1287.00
10	1	2.9	1352.75
11	1	2.8	1309.00
12	1	2.4	1274.00
13	1	3.9	1509.50
14	1	3.7	1525.25
15	1	6.6	1843.00
16	1	3.5	1483.50
17	1	4.1	1541.50
18	1	3.6	1451.25
19	1	2.8	1328.25
20	1	2.0	1206.50
21	1	2.0	1239.50
22	1	2.5	1306.00
23	1	2.3	1326.00
24	1	3.2	1472.75
25	1	4.2	1609.00
26	1	4.2	1610.75
27	1	4.2	1620.50
28	1	3.1	1444.25
29	1	2.6	1418.00
...	...	...	...
215	1	2.2	1099.50
216	1	2.1	1093.75
217	1	2.3	1075.50
218	1	2.6	1151.75
219	1	3.8	1406.75
220	1	4.4	1437.50
221	1	4.5	1424.50
222	1	3.3	1278.50
223	1	2.0	1131.75
224	1	1.1	1006.25
225	1	0.9	982.25
226	1	0.8	968.50
227	1	0.7	940.50
228	1	3.8	1498.25
229	1	3.0	1308.00
230	1	2.7	1209.00
231	1	3.5	1310.25
232	1	2.8	1170.75
233	1	1.9	1112.00
234	1	3.0	1225.00
235	1	1.9	1064.50
236	1	2.7	1236.25
237	1	1.7	1089.00
238	1	1.7	1137.75
239	1	1.5	1097.50
240	1	1.7	1117.50
241	1	2.2	1170.25
242	1	4.5	1501.25
243	1	3.5	1272.50
244	1	1.0	969.50

	w1	w2	w3	w4	t
0	5.1	3.5	1.4	0.2	1
1	4.9	3.0	1.4	0.2	1
2	4.7	3.2	1.3	0.2	1
3	4.6	3.1	1.5	0.2	1
4	5.0	3.6	1.4	0.2	1
5	5.4	3.9	1.7	0.4	1
6	4.6	3.4	1.4	0.3	1
7	5.0	3.4	1.5	0.2	1
8	4.4	2.9	1.4	0.2	1
9	4.9	3.1	1.5	0.1	1
10	5.4	3.7	1.5	0.2	1
11	4.8	3.4	1.6	0.2	1
12	4.8	3.0	1.4	0.1	1
13	4.3	3.0	1.1	0.1	1
14	5.8	4.0	1.2	0.2	1
15	5.7	4.4	1.5	0.4	1
16	5.4	3.9	1.3	0.4	1
17	5.1	3.5	1.4	0.3	1
18	5.7	3.8	1.7	0.3	1
19	5.1	3.8	1.5	0.3	1
20	5.4	3.4	1.7	0.2	1
21	5.1	3.7	1.5	0.4	1
22	4.6	3.6	1.0	0.2	1
23	5.1	3.3	1.7	0.5	1
24	4.8	3.4	1.9	0.2	1
25	5.0	3.0	1.6	0.2	1
26	5.0	3.4	1.6	0.4	1
27	5.2	3.5	1.5	0.2	1
28	5.2	3.4	1.4	0.2	1
29	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...
70	5.9	3.2	4.8	1.8	2
71	6.1	2.8	4.0	1.3	2
72	6.3	2.5	4.9	1.5	2
73	6.1	2.8	4.7	1.2	2
74	6.4	2.9	4.3	1.3	2
75	6.6	3.0	4.4	1.4	2
76	6.8	2.8	4.8	1.4	2
77	6.7	3.0	5.0	1.7	2
78	6.0	2.9	4.5	1.5	2
79	5.7	2.6	3.5	1.0	2
80	5.5	2.4	3.8	1.1	2
81	5.5	2.4	3.7	1.0	2
82	5.8	2.7	3.9	1.2	2
83	6.0	2.7	5.1	1.6	2
84	5.4	3.0	4.5	1.5	2
85	6.0	3.4	4.5	1.6	2
86	6.7	3.1	4.7	1.5	2
87	6.3	2.3	4.4	1.3	2
88	5.6	3.0	4.1	1.3	2
89	5.5	2.5	4.0	1.3	2
90	5.5	2.6	4.4	1.2	2
91	6.1	3.0	4.6	1.4	2
92	5.8	2.6	4.0	1.2	2
93	5.0	2.3	3.3	1.0	2
94	5.6	2.7	4.2	1.3	2
95	5.7	3.0	4.2	1.2	2
96	5.7	2.9	4.2	1.3	2
97	6.2	2.9	4.3	1.3	2
98	5.1	2.5	3.0	1.1	2
99	5.7	2.8	4.1	1.3	2

	constant	w1	w2	w3	w4	t
0	1	5.1	3.5	1.4	0.2	1
1	1	4.9	3.0	1.4	0.2	1
2	1	4.7	3.2	1.3	0.2	1
3	1	4.6	3.1	1.5	0.2	1
4	1	5.0	3.6	1.4	0.2	1
5	1	5.4	3.9	1.7	0.4	1
6	1	4.6	3.4	1.4	0.3	1
7	1	5.0	3.4	1.5	0.2	1
8	1	4.4	2.9	1.4	0.2	1
9	1	4.9	3.1	1.5	0.1	1
10	1	5.4	3.7	1.5	0.2	1
11	1	4.8	3.4	1.6	0.2	1
12	1	4.8	3.0	1.4	0.1	1
13	1	4.3	3.0	1.1	0.1	1
14	1	5.8	4.0	1.2	0.2	1
15	1	5.7	4.4	1.5	0.4	1
16	1	5.4	3.9	1.3	0.4	1
17	1	5.1	3.5	1.4	0.3	1
18	1	5.7	3.8	1.7	0.3	1
19	1	5.1	3.8	1.5	0.3	1
20	1	5.4	3.4	1.7	0.2	1
21	1	5.1	3.7	1.5	0.4	1
22	1	4.6	3.6	1.0	0.2	1
23	1	5.1	3.3	1.7	0.5	1
24	1	4.8	3.4	1.9	0.2	1
25	1	5.0	3.0	1.6	0.2	1
26	1	5.0	3.4	1.6	0.4	1
27	1	5.2	3.5	1.5	0.2	1
28	1	5.2	3.4	1.4	0.2	1
29	1	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...	...
70	1	5.9	3.2	4.8	1.8	2
71	1	6.1	2.8	4.0	1.3	2
72	1	6.3	2.5	4.9	1.5	2
73	1	6.1	2.8	4.7	1.2	2
74	1	6.4	2.9	4.3	1.3	2
75	1	6.6	3.0	4.4	1.4	2
76	1	6.8	2.8	4.8	1.4	2
77	1	6.7	3.0	5.0	1.7	2
78	1	6.0	2.9	4.5	1.5	2
79	1	5.7	2.6	3.5	1.0	2
80	1	5.5	2.4	3.8	1.1	2
81	1	5.5	2.4	3.7	1.0	2
82	1	5.8	2.7	3.9	1.2	2
83	1	6.0	2.7	5.1	1.6	2
84	1	5.4	3.0	4.5	1.5	2
85	1	6.0	3.4	4.5	1.6	2
86	1	6.7	3.1	4.7	1.5	2
87	1	6.3	2.3	4.4	1.3	2
88	1	5.6	3.0	4.1	1.3	2
89	1	5.5	2.5	4.0	1.3	2
90	1	5.5	2.6	4.4	1.2	2
91	1	6.1	3.0	4.6	1.4	2
92	1	5.8	2.6	4.0	1.2	2
93	1	5.0	2.3	3.3	1.0	2
94	1	5.6	2.7	4.2	1.3	2
95	1	5.7	3.0	4.2	1.2	2
96	1	5.7	2.9	4.2	1.3	2
97	1	6.2	2.9	4.3	1.3	2
98	1	5.1	2.5	3.0	1.1	2
99	1	5.7	2.8	4.1	1.3	2

	constant	f_1	f_2	f_3	f_4	f_5	f_6	f_7	output
0	1	5.1	3.5	1.4	0.2	0.04	44.275	3455.15251	1
1	1	4.9	3.0	1.4	0.2	0.04	28.400	2829.15249	1
2	1	4.7	3.2	1.3	0.2	0.04	34.068	2297.95007	1
3	1	4.6	3.1	1.5	0.2	0.04	31.291	2064.22976	1
4	1	5.0	3.6	1.4	0.2	0.04	48.056	3130.00000	1
5	1	5.4	3.9	1.7	0.4	0.16	61.019	4597.25024	1
6	1	4.6	3.4	1.4	0.3	0.09	40.704	2064.42976	1
7	1	5.0	3.4	1.5	0.2	0.04	40.804	3129.90000	1
8	1	4.4	2.9	1.4	0.2	0.04	25.789	1653.46224	1
9	1	4.9	3.1	1.5	0.1	0.01	31.291	2829.35249	1
10	1	5.4	3.7	1.5	0.2	0.04	52.153	4596.85024	1
11	1	4.8	3.4	1.6	0.2	0.04	40.904	2553.03968	1
12	1	4.8	3.0	1.4	0.1	0.01	28.400	2552.43968	1
13	1	4.3	3.0	1.1	0.1	0.01	28.100	1474.18443	1
14	1	5.8	4.0	1.2	0.2	0.04	65.200	6568.76768	1
15	1	5.7	4.4	1.5	0.4	0.16	86.684	6022.82057	1
16	1	5.4	3.9	1.3	0.4	0.16	60.619	4596.85024	1
17	1	5.1	3.5	1.4	0.3	0.09	44.275	3455.15251	1
18	1	5.7	3.8	1.7	0.3	0.09	56.572	6022.42057	1
19	1	5.1	3.8	1.5	0.3	0.09	56.372	3455.55251	1
20	1	5.4	3.4	1.7	0.2	0.04	41.004	4596.75024	1
21	1	5.1	3.7	1.5	0.4	0.16	52.153	3455.45251	1
22	1	4.6	3.6	1.0	0.2	0.04	47.656	2064.22976	1
23	1	5.1	3.3	1.7	0.5	0.25	37.637	3455.25251	1
24	1	4.8	3.4	1.9	0.2	0.04	41.204	2553.33968	1
25	1	5.0	3.0	1.6	0.2	0.04	28.600	3129.60000	1
26	1	5.0	3.4	1.6	0.4	0.16	40.904	3130.00000	1
27	1	5.2	3.5	1.5	0.2	0.04	44.375	3807.04032	1
28	1	5.2	3.4	1.4	0.2	0.04	40.704	3806.84032	1
29	1	4.7	3.2	1.6	0.2	0.04	34.368	2298.25007	1
...	...	...	...	...	...	...	...	...	...
120	1	6.9	3.2	5.7	2.3	5.29	38.468	15649.21349	3
121	1	5.6	2.8	4.9	2.0	4.00	26.852	5515.01776	3
122	1	7.7	2.8	6.7	2.0	4.00	28.652	27077.34157	3
123	1	6.3	2.7	4.9	1.8	3.24	24.583	9931.96543	3
124	1	6.7	3.3	5.7	2.1	4.41	41.637	13510.25107	3
125	1	7.2	3.2	6.0	1.8	3.24	38.768	19358.37632	3
126	1	6.2	2.8	4.8	1.8	3.24	26.752	9168.92832	3
127	1	6.1	3.0	4.9	1.8	3.24	31.900	8453.86301	3
128	1	6.4	2.8	5.6	2.1	4.41	27.552	10745.81824	3
129	1	7.2	3.0	5.8	1.6	2.56	32.800	19357.97632	3
130	1	7.4	2.8	6.1	1.9	3.61	28.052	22198.96624	3
131	1	7.9	3.8	6.4	2.0	4.00	61.272	30780.76399	3
132	1	6.4	2.8	5.6	2.2	4.84	27.552	10745.81824	3
133	1	6.3	2.8	5.1	1.5	2.25	27.052	9932.26543	3
134	1	6.1	2.6	5.6	1.4	1.96	23.176	8454.16301	3
135	1	7.7	3.0	6.1	2.3	5.29	33.100	27076.94157	3
136	1	6.3	3.4	5.6	2.4	5.76	44.904	9933.36543	3
137	1	6.4	3.1	5.5	1.8	3.24	35.291	10746.01824	3
138	1	6.0	3.0	4.8	1.8	3.24	31.800	7783.80000	3
139	1	6.9	3.1	5.4	2.1	4.41	35.191	15648.81349	3
140	1	6.7	3.1	5.6	2.4	5.76	35.391	13509.95107	3
141	1	6.9	3.1	5.1	2.3	5.29	34.891	15648.51349	3
142	1	5.8	2.7	5.1	1.9	3.61	24.783	6571.36768	3
143	1	6.8	3.2	5.9	2.3	5.29	38.668	14548.43568	3
144	1	6.7	3.3	5.7	2.5	6.25	41.637	13510.25107	3
145	1	6.7	3.0	5.2	2.3	5.29	32.200	13509.45107	3
146	1	6.3	2.5	5.0	1.9	3.61	20.625	9931.86543	3
147	1	6.5	3.0	5.2	2.0	4.00	32.200	11611.10625	3
148	1	6.2	3.4	5.4	2.3	5.29	44.704	9170.12832	3
149	1	5.9	3.0	5.1	1.8	3.24	32.100	7157.34299	3

	constant	f_1	f_2	f_3	f_4	f_5	f_6	f_7	output
84	1	5.4	3.0	4.5	1.5	2.25	31.500	4599.15024	2
122	1	7.7	2.8	6.7	2.0	4.00	28.652	27077.34157	3
28	1	5.2	3.4	1.4	0.2	0.04	40.704	3806.84032	1
24	1	4.8	3.4	1.9	0.2	0.04	41.204	2553.33968	1
75	1	6.6	3.0	4.4	1.4	1.96	31.400	12530.72576	2
109	1	7.2	3.6	6.1	2.5	6.25	52.756	19358.87632	3
81	1	5.5	2.4	3.7	1.0	1.00	17.524	5038.94375	2
98	1	5.1	2.5	3.0	1.1	1.21	18.625	3455.75251	2
80	1	5.5	2.4	3.8	1.1	1.21	17.624	5039.04375	2
100	1	6.3	3.3	6.0	2.5	6.25	41.937	9933.66543	3
124	1	6.7	3.3	5.7	2.1	4.41	41.637	13510.25107	3
2	1	4.7	3.2	1.3	0.2	0.04	34.068	2297.95007	1
34	1	4.9	3.1	1.5	0.1	0.01	31.291	2829.35249	1
44	1	5.1	3.8	1.9	0.4	0.16	56.772	3455.95251	1
128	1	6.4	2.8	5.6	2.1	4.41	27.552	10745.81824	3
13	1	4.3	3.0	1.1	0.1	0.01	28.100	1474.18443	1
93	1	5.0	2.3	3.3	1.0	1.00	15.467	3130.60000	2
41	1	4.5	2.3	1.3	0.3	0.09	13.467	1848.88125	1
63	1	6.1	2.9	4.7	1.4	1.96	29.089	8453.56301	2
137	1	6.4	3.1	5.5	1.8	3.24	35.291	10746.01824	3
19	1	5.1	3.8	1.5	0.3	0.09	56.372	3455.55251	1
60	1	5.0	2.0	3.5	1.0	1.00	11.500	3130.50000	2
126	1	6.2	2.8	4.8	1.8	3.24	26.752	9168.92832	3
11	1	4.8	3.4	1.6	0.2	0.04	40.904	2553.03968	1
47	1	4.6	3.2	1.4	0.2	0.04	34.168	2064.22976	1
18	1	5.7	3.8	1.7	0.3	0.09	56.572	6022.42057	1
96	1	5.7	2.9	4.2	1.3	1.69	28.589	6024.02057	2
107	1	7.3	2.9	6.3	1.8	3.24	30.689	20739.91593	3
141	1	6.9	3.1	5.1	2.3	5.29	34.891	15648.51349	3
53	1	5.5	2.3	4.0	1.3	1.69	16.167	5039.14375	2
...	...	...	...	...	...	...	...	...	...
8	1	4.4	2.9	1.4	0.2	0.04	25.789	1653.46224	1
49	1	5.0	3.3	1.4	0.2	0.04	37.337	3129.70000	1
112	1	6.8	3.0	5.5	2.1	4.41	32.500	14547.83568	3
17	1	5.1	3.5	1.4	0.3	0.09	44.275	3455.15251	1
15	1	5.7	4.4	1.5	0.4	0.16	86.684	6022.82057	1
104	1	6.5	3.0	5.8	2.2	4.84	32.800	11611.70625	3
91	1	6.1	3.0	4.6	1.4	1.96	31.600	8453.56301	2
46	1	5.1	3.8	1.6	0.2	0.04	56.472	3455.65251	1
43	1	5.0	3.5	1.6	0.6	0.36	44.475	3130.10000	1
101	1	5.8	2.7	5.1	1.9	3.61	24.783	6571.36768	3
37	1	4.9	3.1	1.5	0.1	0.01	31.291	2829.35249	1
38	1	4.4	3.0	1.3	0.2	0.04	28.300	1653.46224	1
125	1	7.2	3.2	6.0	1.8	3.24	38.768	19358.37632	3
103	1	6.3	2.9	5.6	1.8	3.24	29.989	9932.86543	3
71	1	6.1	2.8	4.0	1.3	1.69	25.952	8452.76301	2
65	1	6.7	3.1	4.4	1.4	1.96	34.191	13508.75107	2
149	1	5.9	3.0	5.1	1.8	3.24	32.100	7157.34299	3
40	1	5.0	3.5	1.3	0.3	0.09	44.175	3129.80000	1
5	1	5.4	3.9	1.7	0.4	0.16	61.019	4597.25024	1
131	1	7.9	3.8	6.4	2.0	4.00	61.272	30780.76399	3
57	1	4.9	2.4	3.3	1.0	1.00	17.124	2830.45249	2
30	1	4.8	3.1	1.6	0.2	0.04	31.391	2552.73968	1
148	1	6.2	3.4	5.4	2.3	5.29	44.704	9170.12832	3
132	1	6.4	2.8	5.6	2.2	4.84	27.552	10745.81824	3
22	1	4.6	3.6	1.0	0.2	0.04	47.656	2064.22976	1
29	1	4.7	3.2	1.6	0.2	0.04	34.368	2298.25007	1
50	1	7.0	3.2	4.7	1.4	1.96	37.468	16814.90000	2
140	1	6.7	3.1	5.6	2.4	5.76	35.391	13509.95107	3
64	1	5.6	2.9	3.6	1.3	1.69	27.989	5513.81776	2
108	1	6.7	2.5	5.8	1.8	3.24	21.425	13509.55107	3

	constant	f_1	f_2	f_3	f_4	f_5	f_6	f_7	output
84	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
122	1	7.7	2.8	6.7	2.0	4.00	28.652	27077.34157	1
28	1	5.2	3.4	1.4	0.2	0.04	40.704	3806.84032	0
24	1	4.8	3.4	1.9	0.2	0.04	41.204	2553.33968	0
75	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
109	1	7.2	3.6	6.1	2.5	6.25	52.756	19358.87632	1
81	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
98	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
80	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
100	1	6.3	3.3	6.0	2.5	6.25	41.937	9933.66543	1
124	1	6.7	3.3	5.7	2.1	4.41	41.637	13510.25107	1
2	1	4.7	3.2	1.3	0.2	0.04	34.068	2297.95007	0
34	1	4.9	3.1	1.5	0.1	0.01	31.291	2829.35249	0
44	1	5.1	3.8	1.9	0.4	0.16	56.772	3455.95251	0
128	1	6.4	2.8	5.6	2.1	4.41	27.552	10745.81824	1
13	1	4.3	3.0	1.1	0.1	0.01	28.100	1474.18443	0
93	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
41	1	4.5	2.3	1.3	0.3	0.09	13.467	1848.88125	0
63	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
137	1	6.4	3.1	5.5	1.8	3.24	35.291	10746.01824	1
19	1	5.1	3.8	1.5	0.3	0.09	56.372	3455.55251	0
60	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
126	1	6.2	2.8	4.8	1.8	3.24	26.752	9168.92832	1
11	1	4.8	3.4	1.6	0.2	0.04	40.904	2553.03968	0
47	1	4.6	3.2	1.4	0.2	0.04	34.168	2064.22976	0
18	1	5.7	3.8	1.7	0.3	0.09	56.572	6022.42057	0
96	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
107	1	7.3	2.9	6.3	1.8	3.24	30.689	20739.91593	1
141	1	6.9	3.1	5.1	2.3	5.29	34.891	15648.51349	1
53	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
...	...	...	...	...	...	...	...	...	...
8	1	4.4	2.9	1.4	0.2	0.04	25.789	1653.46224	0
49	1	5.0	3.3	1.4	0.2	0.04	37.337	3129.70000	0
112	1	6.8	3.0	5.5	2.1	4.41	32.500	14547.83568	1
17	1	5.1	3.5	1.4	0.3	0.09	44.275	3455.15251	0
15	1	5.7	4.4	1.5	0.4	0.16	86.684	6022.82057	0
104	1	6.5	3.0	5.8	2.2	4.84	32.800	11611.70625	1
91	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
46	1	5.1	3.8	1.6	0.2	0.04	56.472	3455.65251	0
43	1	5.0	3.5	1.6	0.6	0.36	44.475	3130.10000	0
101	1	5.8	2.7	5.1	1.9	3.61	24.783	6571.36768	1
37	1	4.9	3.1	1.5	0.1	0.01	31.291	2829.35249	0
38	1	4.4	3.0	1.3	0.2	0.04	28.300	1653.46224	0
125	1	7.2	3.2	6.0	1.8	3.24	38.768	19358.37632	1
103	1	6.3	2.9	5.6	1.8	3.24	29.989	9932.86543	1
71	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
65	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
149	1	5.9	3.0	5.1	1.8	3.24	32.100	7157.34299	1
40	1	5.0	3.5	1.3	0.3	0.09	44.175	3129.80000	0
5	1	5.4	3.9	1.7	0.4	0.16	61.019	4597.25024	0
131	1	7.9	3.8	6.4	2.0	4.00	61.272	30780.76399	1
57	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
30	1	4.8	3.1	1.6	0.2	0.04	31.391	2552.73968	0
148	1	6.2	3.4	5.4	2.3	5.29	44.704	9170.12832	1
132	1	6.4	2.8	5.6	2.2	4.84	27.552	10745.81824	1
22	1	4.6	3.6	1.0	0.2	0.04	47.656	2064.22976	0
29	1	4.7	3.2	1.6	0.2	0.04	34.368	2298.25007	0
50	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
140	1	6.7	3.1	5.6	2.4	5.76	35.391	13509.95107	1
64	0	0.0	0.0	0.0	0.0	0.00	0.000	0.00000	0
108	1	6.7	2.5	5.8	1.8	3.24	21.425	13509.55107	1

	constant	w1	w2	w3	w4	t
0	1	5.1	3.5	1.4	0.2	1
1	1	4.9	3.0	1.4	0.2	1
2	1	4.7	3.2	1.3	0.2	1
3	1	4.6	3.1	1.5	0.2	1
4	1	5.0	3.6	1.4	0.2	1
5	1	5.4	3.9	1.7	0.4	1
6	1	4.6	3.4	1.4	0.3	1
7	1	5.0	3.4	1.5	0.2	1
8	1	4.4	2.9	1.4	0.2	1
9	1	4.9	3.1	1.5	0.1	1
10	1	5.4	3.7	1.5	0.2	1
11	1	4.8	3.4	1.6	0.2	1
12	1	4.8	3.0	1.4	0.1	1
13	1	4.3	3.0	1.1	0.1	1
14	1	5.8	4.0	1.2	0.2	1
15	1	5.7	4.4	1.5	0.4	1
16	1	5.4	3.9	1.3	0.4	1
17	1	5.1	3.5	1.4	0.3	1
18	1	5.7	3.8	1.7	0.3	1
19	1	5.1	3.8	1.5	0.3	1
20	1	5.4	3.4	1.7	0.2	1
21	1	5.1	3.7	1.5	0.4	1
22	1	4.6	3.6	1.0	0.2	1
23	1	5.1	3.3	1.7	0.5	1
24	1	4.8	3.4	1.9	0.2	1
25	1	5.0	3.0	1.6	0.2	1
26	1	5.0	3.4	1.6	0.4	1
27	1	5.2	3.5	1.5	0.2	1
28	1	5.2	3.4	1.4	0.2	1
29	1	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...	...
70	1	5.9	3.2	4.8	1.8	2
71	1	6.1	2.8	4.0	1.3	2
72	1	6.3	2.5	4.9	1.5	2
73	1	6.1	2.8	4.7	1.2	2
74	1	6.4	2.9	4.3	1.3	2
75	1	6.6	3.0	4.4	1.4	2
76	1	6.8	2.8	4.8	1.4	2
77	1	6.7	3.0	5.0	1.7	2
78	1	6.0	2.9	4.5	1.5	2
79	1	5.7	2.6	3.5	1.0	2
80	1	5.5	2.4	3.8	1.1	2
81	1	5.5	2.4	3.7	1.0	2
82	1	5.8	2.7	3.9	1.2	2
83	1	6.0	2.7	5.1	1.6	2
84	1	5.4	3.0	4.5	1.5	2
85	1	6.0	3.4	4.5	1.6	2
86	1	6.7	3.1	4.7	1.5	2
87	1	6.3	2.3	4.4	1.3	2
88	1	5.6	3.0	4.1	1.3	2
89	1	5.5	2.5	4.0	1.3	2
90	1	5.5	2.6	4.4	1.2	2
91	1	6.1	3.0	4.6	1.4	2
92	1	5.8	2.6	4.0	1.2	2
93	1	5.0	2.3	3.3	1.0	2
94	1	5.6	2.7	4.2	1.3	2
95	1	5.7	3.0	4.2	1.2	2
96	1	5.7	2.9	4.2	1.3	2
97	1	6.2	2.9	4.3	1.3	2
98	1	5.1	2.5	3.0	1.1	2
99	1	5.7	2.8	4.1	1.3	2

	w1	w2	w3	w4	t
0	5.1	3.5	1.4	0.2	1
1	4.9	3.0	1.4	0.2	1
2	4.7	3.2	1.3	0.2	1
3	4.6	3.1	1.5	0.2	1
4	5.0	3.6	1.4	0.2	1
5	5.4	3.9	1.7	0.4	1
6	4.6	3.4	1.4	0.3	1
7	5.0	3.4	1.5	0.2	1
8	4.4	2.9	1.4	0.2	1
9	4.9	3.1	1.5	0.1	1
10	5.4	3.7	1.5	0.2	1
11	4.8	3.4	1.6	0.2	1
12	4.8	3.0	1.4	0.1	1
13	4.3	3.0	1.1	0.1	1
14	5.8	4.0	1.2	0.2	1
15	5.7	4.4	1.5	0.4	1
16	5.4	3.9	1.3	0.4	1
17	5.1	3.5	1.4	0.3	1
18	5.7	3.8	1.7	0.3	1
19	5.1	3.8	1.5	0.3	1
20	5.4	3.4	1.7	0.2	1
21	5.1	3.7	1.5	0.4	1
22	4.6	3.6	1.0	0.2	1
23	5.1	3.3	1.7	0.5	1
24	4.8	3.4	1.9	0.2	1
25	5.0	3.0	1.6	0.2	1
26	5.0	3.4	1.6	0.4	1
27	5.2	3.5	1.5	0.2	1
28	5.2	3.4	1.4	0.2	1
29	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...
70	5.9	3.2	4.8	1.8	2
71	6.1	2.8	4.0	1.3	2
72	6.3	2.5	4.9	1.5	2
73	6.1	2.8	4.7	1.2	2
74	6.4	2.9	4.3	1.3	2
75	6.6	3.0	4.4	1.4	2
76	6.8	2.8	4.8	1.4	2
77	6.7	3.0	5.0	1.7	2
78	6.0	2.9	4.5	1.5	2
79	5.7	2.6	3.5	1.0	2
80	5.5	2.4	3.8	1.1	2
81	5.5	2.4	3.7	1.0	2
82	5.8	2.7	3.9	1.2	2
83	6.0	2.7	5.1	1.6	2
84	5.4	3.0	4.5	1.5	2
85	6.0	3.4	4.5	1.6	2
86	6.7	3.1	4.7	1.5	2
87	6.3	2.3	4.4	1.3	2
88	5.6	3.0	4.1	1.3	2
89	5.5	2.5	4.0	1.3	2
90	5.5	2.6	4.4	1.2	2
91	6.1	3.0	4.6	1.4	2
92	5.8	2.6	4.0	1.2	2
93	5.0	2.3	3.3	1.0	2
94	5.6	2.7	4.2	1.3	2
95	5.7	3.0	4.2	1.2	2
96	5.7	2.9	4.2	1.3	2
97	6.2	2.9	4.3	1.3	2
98	5.1	2.5	3.0	1.1	2
99	5.7	2.8	4.1	1.3	2

	constant	w1	w2	w3	w4	t
0	1	5.1	3.5	1.4	0.2	1
1	1	4.9	3.0	1.4	0.2	1
2	1	4.7	3.2	1.3	0.2	1
3	1	4.6	3.1	1.5	0.2	1
4	1	5.0	3.6	1.4	0.2	1
5	1	5.4	3.9	1.7	0.4	1
6	1	4.6	3.4	1.4	0.3	1
7	1	5.0	3.4	1.5	0.2	1
8	1	4.4	2.9	1.4	0.2	1
9	1	4.9	3.1	1.5	0.1	1
10	1	5.4	3.7	1.5	0.2	1
11	1	4.8	3.4	1.6	0.2	1
12	1	4.8	3.0	1.4	0.1	1
13	1	4.3	3.0	1.1	0.1	1
14	1	5.8	4.0	1.2	0.2	1
15	1	5.7	4.4	1.5	0.4	1
16	1	5.4	3.9	1.3	0.4	1
17	1	5.1	3.5	1.4	0.3	1
18	1	5.7	3.8	1.7	0.3	1
19	1	5.1	3.8	1.5	0.3	1
20	1	5.4	3.4	1.7	0.2	1
21	1	5.1	3.7	1.5	0.4	1
22	1	4.6	3.6	1.0	0.2	1
23	1	5.1	3.3	1.7	0.5	1
24	1	4.8	3.4	1.9	0.2	1
25	1	5.0	3.0	1.6	0.2	1
26	1	5.0	3.4	1.6	0.4	1
27	1	5.2	3.5	1.5	0.2	1
28	1	5.2	3.4	1.4	0.2	1
29	1	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...	...
70	1	5.9	3.2	4.8	1.8	2
71	1	6.1	2.8	4.0	1.3	2
72	1	6.3	2.5	4.9	1.5	2
73	1	6.1	2.8	4.7	1.2	2
74	1	6.4	2.9	4.3	1.3	2
75	1	6.6	3.0	4.4	1.4	2
76	1	6.8	2.8	4.8	1.4	2
77	1	6.7	3.0	5.0	1.7	2
78	1	6.0	2.9	4.5	1.5	2
79	1	5.7	2.6	3.5	1.0	2
80	1	5.5	2.4	3.8	1.1	2
81	1	5.5	2.4	3.7	1.0	2
82	1	5.8	2.7	3.9	1.2	2
83	1	6.0	2.7	5.1	1.6	2
84	1	5.4	3.0	4.5	1.5	2
85	1	6.0	3.4	4.5	1.6	2
86	1	6.7	3.1	4.7	1.5	2
87	1	6.3	2.3	4.4	1.3	2
88	1	5.6	3.0	4.1	1.3	2
89	1	5.5	2.5	4.0	1.3	2
90	1	5.5	2.6	4.4	1.2	2
91	1	6.1	3.0	4.6	1.4	2
92	1	5.8	2.6	4.0	1.2	2
93	1	5.0	2.3	3.3	1.0	2
94	1	5.6	2.7	4.2	1.3	2
95	1	5.7	3.0	4.2	1.2	2
96	1	5.7	2.9	4.2	1.3	2
97	1	6.2	2.9	4.3	1.3	2
98	1	5.1	2.5	3.0	1.1	2
99	1	5.7	2.8	4.1	1.3	2

	constant	w1	w2	w3	w4	t
0	1	5.1	3.5	1.4	0.2	1
1	1	4.9	3.0	1.4	0.2	1
2	1	4.7	3.2	1.3	0.2	1
3	1	4.6	3.1	1.5	0.2	1
4	1	5.0	3.6	1.4	0.2	1
5	1	5.4	3.9	1.7	0.4	1
6	1	4.6	3.4	1.4	0.3	1
7	1	5.0	3.4	1.5	0.2	1
8	1	4.4	2.9	1.4	0.2	1
9	1	4.9	3.1	1.5	0.1	1
10	1	5.4	3.7	1.5	0.2	1
11	1	4.8	3.4	1.6	0.2	1
12	1	4.8	3.0	1.4	0.1	1
13	1	4.3	3.0	1.1	0.1	1
14	1	5.8	4.0	1.2	0.2	1
15	1	5.7	4.4	1.5	0.4	1
16	1	5.4	3.9	1.3	0.4	1
17	1	5.1	3.5	1.4	0.3	1
18	1	5.7	3.8	1.7	0.3	1
19	1	5.1	3.8	1.5	0.3	1
20	1	5.4	3.4	1.7	0.2	1
21	1	5.1	3.7	1.5	0.4	1
22	1	4.6	3.6	1.0	0.2	1
23	1	5.1	3.3	1.7	0.5	1
24	1	4.8	3.4	1.9	0.2	1
25	1	5.0	3.0	1.6	0.2	1
26	1	5.0	3.4	1.6	0.4	1
27	1	5.2	3.5	1.5	0.2	1
28	1	5.2	3.4	1.4	0.2	1
29	1	4.7	3.2	1.6	0.2	1
...	...	...	...	...	...	...
70	1	5.9	3.2	4.8	1.8	2
71	1	6.1	2.8	4.0	1.3	2
72	1	6.3	2.5	4.9	1.5	2
73	1	6.1	2.8	4.7	1.2	2
74	1	6.4	2.9	4.3	1.3	2
75	1	6.6	3.0	4.4	1.4	2
76	1	6.8	2.8	4.8	1.4	2
77	1	6.7	3.0	5.0	1.7	2
78	1	6.0	2.9	4.5	1.5	2
79	1	5.7	2.6	3.5	1.0	2
80	1	5.5	2.4	3.8	1.1	2
81	1	5.5	2.4	3.7	1.0	2
82	1	5.8	2.7	3.9	1.2	2
83	1	6.0	2.7	5.1	1.6	2
84	1	5.4	3.0	4.5	1.5	2
85	1	6.0	3.4	4.5	1.6	2
86	1	6.7	3.1	4.7	1.5	2
87	1	6.3	2.3	4.4	1.3	2
88	1	5.6	3.0	4.1	1.3	2
89	1	5.5	2.5	4.0	1.3	2
90	1	5.5	2.6	4.4	1.2	2
91	1	6.1	3.0	4.6	1.4	2
92	1	5.8	2.6	4.0	1.2	2
93	1	5.0	2.3	3.3	1.0	2
94	1	5.6	2.7	4.2	1.3	2
95	1	5.7	3.0	4.2	1.2	2
96	1	5.7	2.9	4.2	1.3	2
97	1	6.2	2.9	4.3	1.3	2
98	1	5.1	2.5	3.0	1.1	2
99	1	5.7	2.8	4.1	1.3	2